Guest consider this, a palindrome is a number that is the same reversed. Eg. 1234567 is not a palindrome because 7654321 is not the same. 11111111 is because it is the same reversed. You want a 7 digit palindrome so you have 7 places to fill.

__ __ __ __ __ __ __

9 x 10 x10x10x1x1x1

Numbers are options^

You cannot fill the 1st spot with 0 So the first and last digit will be eliminated of 0. So there is 9 digits from 1-9. If you choose 9 for the first one the last one must be the same. So the last one is 1 option. Once the options are filled multiple!

\(9 * 10 * 10 *10*1*1*1 = 9000 \)

So there should be 9000 options for 7 digit palindromes! I hope thats correct!